Let $X$ be a smooth variety over some field $k \subset \mathbb{C}$. By a theorem of Grothendieck, one has a canonical isomorphism of complex vector spaces $$ \mathbb{H}^j(X, \Omega_{X/k}^\bullet) \otimes_k \mathbb{C} \stackrel{\sim}{\longrightarrow} \mathbb{H}^j(X(\mathbb{C}), \Omega^\bullet_{X^{an}/\mathbb{C}}) $$ between algebraic and analytic de Rham cohomology.

The situation with coefficients is more subtle. If $\nabla: E \to E \otimes_k \Omega^1_U$ is some integrable connection on a locally free sheaf $E$ on $X$, there is still a canonical morphism $$ \mathbb{H}^j(X, (E \otimes \Omega_{X/k}^\bullet, \nabla)) \otimes_k \mathbb{C} \longrightarrow \mathbb{H}^j(X(\mathbb{C}), (E^{an} \otimes \Omega^\bullet_{X^{an}/\mathbb{C}}, \nabla^{an})) \quad \quad (\ast) $$ between the algebraic (hyper)cohomology of the complex induced by the connection and the corresponding analytic one.

Deligne proves that this is an isomorphism when $\nabla$ has regular singularities.

**Question**: is this theorem and "if and only if", that is, if the map (*) is an isomorphism, is it true that $\nabla$ has regular singularities?

If this is the case, a reference would be very much appreciated.